I. Stetcu

Recent developments in no-core shell-model calculations

We present an overview of recent results and developments of the no-core shell model (NCSM), an ab initio approach to the nuclear many-body problem for light nuclei. In this approach, we start from realistic two-nucleon or two- plus three-nucleon interactions. Many-body calculations are performed using a finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic inter-nucleon interactions that generate strong short-range correlations, we derive effective interactions by unitary transformations that are tailored to the HO basis truncation. For soft realistic interactions, this might not be necessary. If this is the case, the NCSM calculations are variational. In either case, the ab initio NCSM preserves translational invariance of the nuclear many-body problem. In this review, we, in particular, highlight results obtained with the chiral two- plus three-nucleon interactions. We discuss efforts to extend the applicability of the NCSM to heavier nuclei and larger model spaces using importance-truncation schemes and/or use of effective interactions with a core. We outline an extension of the ab initio NCSM to the description of nuclear reactions by the resonating group method technique. A future direction of the approach, the ab initio NCSM with continuum, which will provide a complete description of nuclei as open systems with coupling of bound and continuum states, is given in the concluding part of the review.

Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory

Recent calculations of EDMs of light nuclei in the framework of chiral effective field theory are presented. We argue that they can be written in terms of the leading six low-energy constants encoding CP-violating physics. EDMs of the deuteron, triton, and helion are explicitly given in order to corroborate our claim. An eventual non-zero measurement of these EDMs can be used to disentangle the different sources and strengths of CP-violation.

Three and four harmonically trapped particles in an effective-field-theory framework

We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body interactions, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the no-core shell model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods (in the four-body case). We also present results for finite scattering lengths and nonzero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.

Effective interactions for light nuclei: An Effective (field theory) approach

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered.

Effective operators from exact many-body renormalization

We construct effective two-body Hamiltonians and E2 operators for the p shell by performing 16h Q ab initio no-core shell model (NCSM) calculations for A = 5 and A = 6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the 0hΩ space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.

Effective interactions and operators in the no-core shell model

Solutions to the nuclear many-body problem rely on effective interactions, and in general effective operators, to take into account effects not included in calculations. These include effects due to the truncation to finite model spaces where a numerical calculation is tractable, as well as physical terms not included in the description in the first place. In the no-core shell model (NCSM) framework, we discuss two approaches to the effective interactions based on (i) unitary transformations and (ii) effective field theory (EFT) principles. Starting from a given Hamiltonian, the unitary transformation approach is designed to take into account effects induced by the truncation to finite model spaces in which a numerical calculation is performed. This approach was widely applied to the description of nuclear properties of light nuclei; we review the theory and present representative results. In the EFT approach, a Hamiltonian is always constructed in a truncated model space according to the symmetries of the underlying theory, making use of power counting to limit the number of interactions included in the calculations. Hence, physical terms not explicitly included in the calculation are treated on the same footing with the truncation to a finite model space. In this approach, we review results for both nuclear and trapped atomic systems, for which the effective theories are formally similar, albeit describing different underlying physics. Finally, the application of the EFT method of constructing effective interactions to the Gamow shell model is briefly discussed.

Ab initio shell model with a core: Extending the No Core Shell Model to heavier nuclei

The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of atomic nuclei, starting with the fundamental interactions among the nucleons and treating all A nucleons as being active. This approach has been successfully applied to nuclei with A ≤ 20, but it is difficult to treat heavier mass nuclei with existing computer technology, because of the extemely large basis spaces required to obtain converged results. In this presentation we outline a new formalism for extending the NCSM to heavier mass nuclei. It involves using the NCSM approach to determine the core, one-body and two-body (and perhaps also three-body) terms, which are the usual input for standard shell model (SSM) calculations. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. As a test of this new formalism, we apply it to nuclei in the 0p-shell, for which exact NCSM calculations can also be performed for making comparisons. Results are given both for energy spectra and electromagnetic properties.

Collapse of the random-phase approximation: Examples and counter-examples from the shell model

The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a ``phase transition in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as ``collapse of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.